81/80: Difference between revisions

Godtone (talk | contribs)
m don't remove the temperaments section, one should at bare minimum be able to find the meantone family from this page easily
Cmloegcmluin (talk | contribs)
add section for this comma's use in Sagittal notation
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== Approximation ==
== Approximation ==
If one wants to treat the syntonic comma as a musical interval in its own right as opposed to tempering it out, one can easily use it in melodies as either an {{w|appoggitura}}, an {{w|acciaccatura}}, or a quick passing tone. It is also very easy to exploit in [[comma pump]] modulations, as among the [[Meantone comma pump examples|known examples]] of this kind of thing are familiar-sounding chord progressions.  Furthermore, not tempering out 81/80 both allows wolf intervals like [[40/27]] and [[27/20]] to be deliberately exploited as dissonances to be resolved, and it also allows one to contrast intervals like 5/4 and [[81/64]]. The [[barium]] temperament exploits the comma by setting it equal to exactly 1/56th of the octave.
If one wants to treat the syntonic comma as a musical interval in its own right as opposed to tempering it out, one can easily use it in melodies as either an {{w|appoggitura}}, an {{w|acciaccatura}}, or a quick passing tone. It is also very easy to exploit in [[comma pump]] modulations, as among the [[Meantone comma pump examples|known examples]] of this kind of thing are familiar-sounding chord progressions.  Furthermore, not tempering out 81/80 both allows wolf intervals like [[40/27]] and [[27/20]] to be deliberately exploited as dissonances to be resolved, and it also allows one to contrast intervals like 5/4 and [[81/64]]. The [[barium]] temperament exploits the comma by setting it equal to exactly 1/56th of the octave.
== Sagittal notation ==
In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal | \! }} and is called the '''5 comma''', or '''5C''' for short, because the simplest ratio it notates is 4:5, as for example in C:E{{sagittal | \! }}.


== Relations to other superparticular ratios ==
== Relations to other superparticular ratios ==